Finite Group Databasebeta

← #19138136

Subgroups — #19138136

Order 5504.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063300C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic, complemented
3C2×#13063295C211yesmaximal, characteristic, complemented
4C2×#13063295C211yesmaximal, characteristic, complemented
5C2×C4×D172C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
7#14582821C211yesmaximal, characteristic, complemented
8#14582815C211yesmaximal, characteristic, complemented
9#14582815C211yesmaximal, characteristic, complemented
10#14582809C211yesmaximal, characteristic, complemented
11#14582801C211yesmaximal, characteristic, complemented
12#14582777C211yesmaximal, characteristic, complemented
13#14582777C211yesmaximal, characteristic, complemented
14#14582773C211yesmaximal, characteristic, complemented
15C43×#388C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×D172C2211yescharacteristic
20C22×D172C2211yescharacteristic
21C22×D172C2211yescharacteristic, complemented
22C22×C22⋊D43C2211yescharacteristic
23C22×C22⋊D43C2211yescharacteristic
24C22×C4×D43C2211yescharacteristic
25C22×C4×D43C2211yescharacteristic
26C22×C4×D43C2211yescharacteristic, complemented
27#13063300—24no—
28#13063298—24no—
29#13063295—24no—
30#13063295—24no—
31C4×D172—24no—
32C2×C4⋊Dic43C2211yescharacteristic, complemented
33C2×C4⋊Dic43C2211yescharacteristic, complemented
34C2×Dic43⋊C4C2211yescharacteristic, complemented
35C2×C22⋊Dic43C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
47C22⋊C4×D43—24no—
48C43⋊#95C2211yescharacteristic, complemented
49C43⋊#95C2211yescharacteristic, complemented
50C2×C4⋊C4×C43C2211yescharacteristic, complemented
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C42×C43C2211yescharacteristic, complemented
55#95×C43C2211yescharacteristic, complemented
56#95×C43C2211yescharacteristic, complemented
57C24×C43C2311yescharacteristic
58C23×D43—22no—
59C23×D43—22no—
60C23×D43—22no—
61C23×D43—22no—
62C23×D43—22no—
63C23×D43—41no—
64C23×D43—41no—
65C23×D43C2311yescharacteristic
66C23×D43C2311yescharacteristic
67C23×D43C2311yescharacteristic
68C23×D43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C22×C4×C43C2311yescharacteristic
71C22×C4×C43C2311yescharacteristic
72C22×C4×C43C2311yescharacteristic
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C2×C22⋊D43—22no—
76C2×C22⋊D43—22no—
77C2×C22⋊D43—22no—
78C2×C22⋊D43—22no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C22×Dic43C2311yescharacteristic
82C22×Dic43C2311yescharacteristic
83C22×Dic43C2311yescharacteristic
84C22×Dic43C2311yescharacteristic
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—22no—
89C2×D172—22no—
90C2×D172—22no—
91C2×D172—22no—
92C2×D172—22no—
93C2×D172—22no—
94C2×D172—22no—
95C2×D172—22no—
96C2×D172—41no—
97C2×D172—41no—
98C2×D172—41no—
99C2×D172D414yescomplemented
100C2×C4×D43—22no—
101C2×C4×D43—22no—
102C2×C4×D43—22no—
103C2×C4×D43—22no—
104C2×C4×D43—22no—
105C2×C4×D43—22no—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108C2×C4×D43—41no—
109C4⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—22no—
112C22⋊C4×C43D414yescomplemented
113C42×C43—22no—
114C22⋊Dic43—22no—
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—22no—
118(C2×D43)⋊C4—22no—
119(C2×D43)⋊C4—22no—
120(C2×D43)⋊C4—22no—
121(C2×D43)⋊C4—22no—
122(C2×D43)⋊C4—22no—
123(C2×D43)⋊C4—22no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4D414yescomplemented
126C4⋊Dic43—22no—
127C4⋊Dic43—41no—
128Dic43⋊C4—22no—
129C23×C43—21no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43C2×D412yes—
136C23×C43C2411yescharacteristic
137C22×D43—21no—
138C22×D43—21no—
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—28no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146C22×D43—21no—
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—21no—
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—21no—
157C22×D43—21no—
158C22×D43—21no—
159C22×D43—21no—
160C22×D43—21no—
161C22×D43—44no—
162C22×D43—44no—
163C22×D43—44no—
164C22×D43—44no—
165C22×D43—44no—
166C22×D43—44no—
167C22×D43C2×D412yes—
168C22×D43C2×D412yes—
169C22×D43C2×D412yes—
170C22×D43#4112yes—
171C22×D43#4112yes—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—21no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43C2×D412yes—
187C2×C4×C43C2×D412yes—
188C2×C4×C43C2×D412yes—
189C2×C4×C43C2×D412yes—
190C22⋊D43—44no—
191C22⋊D43—44no—
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—21no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43C2×D412yes—
204D172—28no—
205D172—44no—
206D172—44no—
207D172—44no—
208D172—44no—
209C4×D43—44no—
210C4×D43—44no—
211C4×D43—44no—
212C22×C43—22no—
213C22×C43—22no—
214C22×C43—22no—
215C22×C43—41no—
216C22×C43—41no—
217C22×C43—41no—
218C22×C43—41no—
219C22×C43C22×D411yescharacteristic
220C22×C43C22×D411yescharacteristic
221C22×C43C22×D411yescharacteristic
222C22×C43C2×#4111yescharacteristic
223C22×C43C2×#4111yescharacteristic
224C22×C43H(5,𝔽2)11yescharacteristic
225C22×C43H(5,𝔽2)11yescharacteristic
226C2×D43—22no—
227C2×D43—22no—
228C2×D43—22no—
229C2×D43—22no—
230C2×D43—22no—
231C2×D43—22no—
232C2×D43—22no—
233C2×D43—22no—
234C2×D43—22no—
235C2×D43—22no—
236C2×D43—22no—
237C2×D43—22no—
238C2×D43—416no—
239C2×D43—41no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C2×D43—41no—
246C2×D43—41no—
247C2×D43—41no—
248C2×D43—41no—
249C2×D43—41no—
250C2×D43—41no—
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—41no—
254C2×D43#12114yescomplemented
255C4×C43—22no—
256C4×C43—22no—
257C4×C43—22no—
258C4×C43—22no—
259C4×C43—41no—
260C4×C43—41no—
261Dic43—22no—
262Dic43—41no—
263Dic43—41no—
264Dic43—41no—
265#2424—431nomaximal, Sylow
266C2×C43—42no—
267C2×C43C2×#12111yescharacteristic
268C2×C43#52511yescharacteristic
269C2×C43#53811yescharacteristic
270C2×C43D4211yescharacteristic
271C2×C43D4211yescharacteristic
272C2×C43#54611yescharacteristic
273C2×C43#54611yescharacteristic
274D43—24no—
275D43—42no—
276D43—42no—
277D43—81no—
278C2×#121—431no—
279C2×#121—431no—
280C2×#120—431no—
281C2×#120—431no—
282C2×C4×D4—431no—
283C22×C22⋊C4—431no—
284#396—431no—
285#394—431no—
286#394—431no—
287#392—431no—
288#390—431no—
289#388D4311yescharacteristic, complemented
290#386—431no—
291#386—431no—
292#385—431no—
293C43#242411yescharacteristic, complemented, Sylow
294C25—431no—
295C22×D4—431no—
296C22×D4—431no—
297C22×D4—431no—
298C22×D4—431no—
299C22×D4—431no—
300C22×D4—431no—
301C22×D4—431no—
302C23×C4—431no—
303C23×C4—431no—
304C23×C4—431no—
305#121—864no—
306#121—864no—
307#120—864no—
308#120—864no—
309C4×D4—864no—
310C2×C4⋊C4—431no—
311C2×C4⋊C4—431no—
312C2×C4⋊C4—431no—
313C2×C4⋊C4C2×D4311yescharacteristic, complemented
314C2×C22⋊C4—431no—
315C2×C22⋊C4—431no—
316C2×C22⋊C4—431no—
317C2×C22⋊C4—431no—
318C2×C22⋊C4—431no—
319C2×C22⋊C4—431no—
320C2×C22⋊C4—431no—
321C2×C22⋊C4—431no—
322C2×C22⋊C4—431no—
323C2×C22⋊C4—431no—
324C2×C22⋊C4—431no—
325C2×C22⋊C4—431no—
326C2×C22⋊C4—864no—
327C2×C22⋊C4C2×D4311yescharacteristic
328C2×C22⋊C4C2×D4311yescharacteristic
329C2×C22⋊C4C2×D4311yescharacteristic
330C2×C42C2×D4311yescharacteristic, complemented
331#95—431no—
332#95—431no—
333#95C2×D4311yescharacteristic, complemented
334#95C2×D4311yescharacteristic, complemented
335C24—431no—
336C24—431no—
337C24—431no—
338C24—431no—
339C24—862no—
340C24—862no—
341C24—862no—
342C24—862no—
343C24—862no—
344C24—1721no—
345C24—1721no—
346C24C22×D4311yescharacteristic
347C2×D4—434no—
348C2×D4—862no—
349C2×D4—862no—
350C2×D4—862no—
351C2×D4—862no—
352C2×D4—862no—
353C2×D4—862no—
354C2×D4—862no—
355C2×D4—862no—
356C2×D4—862no—
357C2×D4—862no—
358C2×D4—862no—
359C2×D4—862no—
360C2×D4—862no—
361C2×D4—862no—
362C2×D4—862no—
363C2×D4—1721no—
364C2×D4—1721no—
365C2×D4—1721no—
366C2×D4—1721no—
367C2×D4—1721no—
368C22×C4—431no—
369C22×C4—431no—
370C22×C4—431no—
371C22×C4—431no—
372C22×C4—862no—
373C22×C4—862no—
374C22×C4—862no—
375C22×C4—862no—
376C22×C4—862no—
377C22×C4—862no—
378C22×C4—1721no—
379C22×C4—1721no—
380C22×C4—1721no—
381C22×C4C22×D4311yescharacteristic
382C22×C4C22×D4311yescharacteristic
383C22×C4C22×D4311yescharacteristic
384C22×C4C22×D4311yescharacteristic
385C22×C4C22×D4311yescharacteristic
386C22×C4C22×D4311yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—862no—
389C4⋊C4—862no—
390C4⋊C4—1721no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—434no—
394C22⋊C4—862no—
395C22⋊C4—862no—
396C22⋊C4—862no—
397C22⋊C4—862no—
398C22⋊C4—862no—
399C22⋊C4—862no—
400C22⋊C4—862no—
401C22⋊C4—862no—
402C22⋊C4—862no—
403C22⋊C4—862no—
404C22⋊C4—1721no—
405C22⋊C4D17214yescomplemented
406C42—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—432no—
414C23—432no—
415C23—432no—
416C23—432no—
417C23—432no—
418C23—868no—
419C23—861no—
420C23—861no—
421C23—861no—
422C23—861no—
423C23—861no—
424C23—861no—
425C23—861no—
426C23—861no—
427C23—861no—
428C23—861no—
429C23—861no—
430C23—861no—
431C23—861no—
432C23—861no—
433C23—861no—
434C23—861no—
435C23—861no—
436C23—861no—
437C23—861no—
438C23—861no—
439C23—861no—
440C23—861no—
441C23—861no—
442C23—1724no—
443C23—1724no—
444C23—1724no—
445C23—1724no—
446C23—1724no—
447C23—1724no—
448C23C2×D17212yes—
449C23C23×D4311yescharacteristic
450D4—868no—
451D4—1724no—
452D4—1724no—
453D4—1724no—
454D4—1724no—
455D4—1724no—
456D4—1724no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—432no—
472C2×C4—861no—
473C2×C4—861no—
474C2×C4—861no—
475C2×C4—861no—
476C2×C4—861no—
477C2×C4—861no—
478C2×C4—861no—
479C2×C4—861no—
480C2×C4—861no—
481C2×C4—861no—
482C2×C4—861no—
483C2×C4—1724no—
484C2×C4—1724no—
485C2×C4—1724no—
486C2×C4C2×D17212yes—
487C2×C4C2×D17212yes—
488C2×C4D4×D4312yes—
489C2×C4D4×D4312yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—434no—
498C22—862no—
499C22—862no—
500C22—862no—
501C22—862no—
502C22—862no—
503C22—862no—
504C22—862no—
505C22—862no—
506C22—862no—
507C22—862no—
508C22—862no—
509C22—862no—
510C22—17216no—
511C22—1721no—
512C22—1721no—
513C22—1721no—
514C22—1721no—
515C22—1721no—
516C22—1721no—
517C22—1721no—
518C22—1721no—
519C22—1721no—
520C22—1721no—
521C22—1721no—
522C22—1721no—
523C22—1721no—
524C22—1721no—
525C22—1721no—
526C22C2×D4×D4311yescharacteristic
527C22C2×D4×D4311yescharacteristic
528C22C22×D17211yescharacteristic
529C22#41×D4311yescharacteristic
530C22#41×D4311yescharacteristic
531C22#1306337111yescharacteristic
532C22#1306337111yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—862no—
540C4—1721no—
541C4—1721no—
542C4—1721no—
543C2—42no—
544C2—864no—
545C2—3441no—
546C2—1722no—
547C2—1722no—
548C2#121×D4311yescharacteristic
549C2#1458341111yescharacteristic
550C2#1458348811yescharacteristic
551C2D4×D17211yescharacteristic
552C2D4×D17211yescharacteristic
553C2#1458354111yescharacteristic
554C2#1458354211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#388C2
hypercenter#388D43
hypocenterC43#2424
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#13063300C2semidirect
2. C2×#13063298C2semidirect
3. C2×#13063295C2semidirect
4. C2×#13063295C2semidirect
5. C2×C4×D172C2semidirect
6. C2×C22⋊C4×D43C2semidirect
7. #14582821C2semidirect
8. #14582815C2semidirect
9. #14582815C2semidirect
10. #14582809C2semidirect
11. #14582801C2semidirect
12. #14582777C2semidirect
13. #14582777C2semidirect
14. #14582773C2semidirect
15. C43×#388C2semidirect
21. C22×D172C22semidirect
26. C22×C4×D43C22semidirect
32. C2×C4⋊Dic43C22semidirect
33. C2×C4⋊Dic43C22semidirect
34. C2×Dic43⋊C4C22semidirect
42. C2×(C2×D43)⋊C4C22semidirect
43. C2×(C2×D43)⋊C4C22semidirect
44. C2×(C2×D43)⋊C4C22semidirect
45. C2×(C2×D43)⋊C4C22semidirect
46. C2×(C2×D43)⋊C4C22semidirect
48. C43⋊#95C22semidirect
49. C43⋊#95C22semidirect
50. C2×C4⋊C4×C43C22semidirect
54. C2×C42×C43C22semidirect
55. #95×C43C22semidirect
56. #95×C43C22semidirect
99. C2×D172D4semidirect
112. C22⋊C4×C43D4semidirect
125. (C2×D43)⋊C4D4semidirect
254. C2×D43#121semidirect
289. #388D43semidirect
293. C43#2424semidirect
313. C2×C4⋊C4C2×D43semidirect
330. C2×C42C2×D43semidirect
333. #95C2×D43semidirect
334. #95C2×D43semidirect
405. C22⋊C4D172semidirect